Freeze the flank steak 15–20 minutes until firm at the edges. Slice very thin (1/4 inch) against the grain. Toss with 1 teaspoon cornstarch and 1 tablespoon soy sauce; rest while you prep.
Whisk the remaining soy sauce, beef broth, brown sugar, oyster sauce, 1 tablespoon cornstarch, rice vinegar, and sesame oil in a bowl until dissolved.
Blanch broccoli in well-salted boiling water for 90 seconds until vivid green. Transfer to ice water, then drain well.
Heat a large skillet or wok over high heat until smoking. Add 1 tablespoon oil, sear half the beef in a single layer 60–90 seconds per side. Repeat with remaining oil and beef.
Lower to medium heat. Stir the garlic, ginger, and red pepper flakes for 30 seconds until fragrant.
Return beef and broccoli to the pan. Re-whisk the sauce, pour over, and simmer 2–3 minutes until the sauce turns glossy and thick. Serve immediately over jasmine rice with sesame seeds and scallions.